This paper focuses on channel prediction techniques for massive multiple-input multiple-output (MIMO) systems. Previous channel predictors are based on theoretical channel models, which would be deviated from realistic channels. In this paper, we develop and compare a vector Kalman filter (VKF)-based channel predictor and a machine learning (ML)-based channel predictor using the realistic channels from the spatial channel model (SCM), which has been adopted in the 3GPP standard for years. First, we propose a low-complexity mobility estimator based on the spatial average using a large number of antennas in massive MIMO. The mobility estimate can be used to determine the complexity order of developed predictors. The VKF-based channel predictor developed in this paper exploits the autoregressive (AR) parameters estimated from the SCM channels based on the Yule-Walker equations. Then, the ML-based channel predictor using the linear minimum mean square error (LMMSE)-based noise pre-processed data is developed. Numerical results reveal that both channel predictors have substantial gain over the outdated channel in terms of the channel prediction accuracy and data rate. The ML-based predictor has larger overall computational complexity than the VKF-based predictor, but once trained, the operational complexity of ML-based predictor becomes smaller than that of VKF-based predictor.